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Mr. Jones has devised a gambling system for winning at roulette. When he bets, he bets on red and places a bet only when the 10previous spins of the roulette have landed on a black number. He reasons that his chance of winning is quite large because the probability of 11consecutive spins resulting in black is quite small. What do you think of this system?

Short Answer

Expert verified

The wheel has no memory and the probability of win is1/2.

Step by step solution

01

Step: 1 Probability of success:

The probability of success is 1/2.

Although the chances of 11consecutive black numbers in roulette is low, when 10 consecutive black numbers have been witnessed, the result space only contains 10or more consecutive black numbers, making 11 a strong possibility.

P(11consecutive black numbers)

02

Step: 2 probability of success:

The success rate is a statistical term that is widely utilised in the pharmaceutical business, as well as by health authorities to aid decision-making. The idea of success probability is directly connected to conditional power and predictive power.

03

Step: 3 Probability:

In actuality, he stakes his money on:

P(11consecutive black numbers∣10consecutive black numbers)=12

Because the 11th roll is independent of the previous ten, the chance of a red number is 1/2as a consequence.

Another way to put it is that the roulette wheel has no "memory," that is, it flashes red with probability 1/2regardless of the previous ten results.

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